The present invention relates to a process simulation method, and more particularly to a process simulation method for calculating a surface oxidant concentration in an oxidation process for fabricating a semiconductor device.
Process simulations are the techniques for prediction of internal physical quantities such as impurity concentration profile of a transistor or shapes thereof by conducting calculations of fabrication processes of the transistor. A process simulator is used for optimization of the transistor to enable the transistor to exhibit best performances. The use of the process simulator results in remarkable reductions in the cost and the time as compared to the experimental manufacturing of a large scale integrated circuit.
The process simulator implements calculations of the fabrication processes of various semiconductor device by use of computer. Optimum simulation models are incorporated for every processes. For example, the process simulation method for the oxidation process is disclosed in VLSI Design/Manufacturing Simulation, 1987, CMC, pp. 51-62, wherein variation in thickness of the silicon oxide film over time is simulated by solving the following equation (1) which has been obtained by differentiating Deal-Grove Equation. EQU DT.sub.ox /dt=B/(2T.sub.ox.sup.old +A) (1)
t: oxidation time PA1 T.sub.ox : thickness of oxide film at a current time PA1 T.sub.ox.sup.old : thickness of oxide film at an old time PA1 A and B: parameters for oxidation rate.
This method is limited to provide a one-dimensional simulation, but is incapable of providing two or three dimensional simulation.
In the actual LIS circuits, it is required to form local oxidation of silicon layer (LOCOS oxide film) or trench isolation for electrical isolations between individual devices which should be integrated. This means that it is also required to conduct two-dimensional process simulations for the LOCOS oxide film or the trench isolation and also conduct two-dimensional simulations for oxidation over the substrate including isolation regions. The two-dimensional process simulation for the LOCOS oxide film is disclosed in "Semiconductor Process Device Simulation Technique", published from Realize Co. pp. 78-89.
FIG. 1 is a flow chart illustrative of the above conventional two-dimensional process simulation method for oxidation. FIG. 2 is a fragmentary cross sectional elevation view illustrative of silicon oxidation processes. The above conventional two-dimensional process simulation method will be described in detail with reference to FIGS. 1 and 2. In a first step 301, the time for calculating the oxidation is set zero. In a second step 302, an initial oxidation film T.sub.ox.sup.init is given so that an interface of silicon to be oxidized is not made into contact with oxygen atmosphere. This initial oxidation film is required for calculating a surface oxidant concentration in the following third step 303.
In the third step 303, the following oxidant diffusion equation (Laplace equation) in oxide film is solved to find a surface oxidant concentration on an interface between silicon and silicon oxide. EQU D.sub.ox .gradient..sup.2 C.sub.ox =0 (2)
where D.sub.ox is the diffusion coefficient of oxidant in oxide film, .gradient..sup.2 is the Laplacean, and C.sub.ox is the oxidant concentration.
In the fourth step 304, the oxidation calculating time t is put forwarded by an increment .DELTA.t.
In the fifth step, the silicon surface oxidant concentration C.sub.surf is used to solve the following equation to find an oxidation rate dT.sub.ox /dt on the silicon surface. EQU dT.sub.ox /dt=K.times.C.sub.surf (3)
In the sixth step, based upon the oxidation rate dT.sub.ox /dt on the silicon surface and the time increment .DELTA.t, a thickness .gradient.T.sub.ox of oxidized film is found. Further, dT.sub.ox.sup.trans is calculated to form a fresh interface between the silicon oxide and silicon as shown in FIG. 2B.
In the seventh step 307, a deformation calculation is made to find the oxide film thickness as shown in FIG. 2C.
In the eighth step 308, it is verified whether the oxidation calculation time reaches a predetermined final time. If verified, then the simulation is finished. If not verified, then the simulation step enters into the next ninth step 309, wherein for the deformed oxide film, the oxidant diffusion equation is solved to calculate the oxidant surface concentration C.sub.surf on the silicon surface so that a sequential set of the above steps 304 to 308 is repeated until the oxidation calculation time reaches the predetermined final time.
Since in the above conventional process simulation method, the oxidant diffusion equation in the oxide film in the form of Laplace equation is solved to calculate the surface oxidant concentration on the silicon surface or the interface between the silicon and silicon oxide, it is required that a silicon oxide film having a finite or not zero thickness exists in the initial state where the time is zero. Thus, it is required to provide or deposit an initial silicon oxide film previously. This means that it is necessary to input the data for the initial silicon oxide film by user. This previous depositions of the initial silicon oxide film requires various processings. For example, the actual wafer has a surface irregularity or has convex and concave, for which reason if a uniform-thickness silicon oxide film is deposited as an initial silicon oxide film over the wafer, then at the concave portion deposited silicon oxide films overlapped each other. Such overlap of the deposited silicon oxide films as the initial films should be avoided. The various processings by the user side are required for avoiding the above problems. Otherwise, the process simulator receives the load of processings.
In the above circumstances, it had been required to develop a novel process simulation method free from the above problems.